The OEIS mourns the passing of Jim Simons and is grateful to the Simons Foundation for its support of research in many branches of science, including the OEIS.
login
The OEIS is supported by the many generous donors to the OEIS Foundation.

 

Logo
Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A135861 a(n) = binomial(n*(n+1),n)/(n+1). 12
1, 1, 5, 55, 969, 23751, 749398, 28989675, 1329890705, 70625252863, 4263421511271, 288417894029200, 21616536107173175, 1778197364075525550, 159297460456229992380, 15438280311293473537331, 1609484153977526457766689, 179612918129148904884024975 (list; graph; refs; listen; history; text; internal format)
OFFSET
0,3
LINKS
FORMULA
a(n) = A135860(n)/(n+1).
a(n) = [x^(n^2)] 1/(1 - x)^n. - Ilya Gutkovskiy, Oct 10 2017
a(p) == 1 ( mod p^4 ) for prime p >= 5 and a(2*p) == 4*p + 1 ( mod p^4 ) for prime p >= 5 (apply Mestrovic, equation 37). - Peter Bala, Feb 23 2020
a(n) ~ exp(n + 1/2) * n^(n - 3/2) / sqrt(2*Pi). - Vaclav Kotesovec, Oct 17 2020
MAPLE
A135861:=n->binomial(n*(n+1), n)/(n+1); seq(A135861(n), n=0..15); # Wesley Ivan Hurt, May 08 2014
MATHEMATICA
Table[Binomial[n*(n + 1), n]/(n + 1), {n, 0, 15}]
PROG
(PARI) a(n)=binomial(n*(n+1), n)/(n+1)
CROSSREFS
Sequence in context: A195513 A172493 A155807 * A141361 A203013 A266481
KEYWORD
nonn
AUTHOR
Paul D. Hanna, Dec 02 2007
STATUS
approved

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recents
The OEIS Community | Maintained by The OEIS Foundation Inc.

License Agreements, Terms of Use, Privacy Policy. .

Last modified June 13 15:40 EDT 2024. Contains 373389 sequences. (Running on oeis4.)